TPTP Problem File: PLA054_4.p
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- Solve Problem
%------------------------------------------------------------------------------
% File : PLA054_4 : TPTP v9.0.0. Released v8.2.0.
% Domain : Planning
% Problem : Abductive planning: Safe problem
% Version : [QMLTP] axioms.
% English :
% Refs : [Sto98] Stone (1998), Abductive Planning with Sensing
% : [RO12] Raths & Otten (2012), The QMLTP Problem Library for Fi
% Source : [QMLTP]
% Names : APM005+1 [QMLTP]
% Status : Theorem
% Rating : 0.00 v8.2.0
% Syntax : Number of formulae : 21 ( 3 unt; 11 typ; 0 def)
% Number of atoms : 42 ( 0 equ)
% Maximal formula atoms : 16 ( 4 avg)
% Number of connectives : 35 ( 3 ~; 1 |; 12 &)
% ( 0 <=>; 19 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 6 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 13 ( 6 >; 7 *; 0 +; 0 <<)
% Number of predicates : 6 ( 6 usr; 0 prp; 2-3 aty)
% Number of functors : 4 ( 4 usr; 4 con; 0-0 aty)
% Number of variables : 27 (; 22 !; 5 ?; 27 :)
% SPC : TF0_THM_NEQ_NAR
% Comments : Generated by embedproblem, version 1.7.14, rigid constant,
% modal_system_S4, TFF embedding.
%------------------------------------------------------------------------------
tff('$ki_world_type',type,
'$ki_world': $tType ).
tff('$ki_local_world_decl',type,
'$ki_local_world': '$ki_world' ).
tff('$ki_accessible_decl',type,
'$ki_accessible': ( '$ki_world' * '$ki_world' ) > $o ).
tff(mrel_reflexive,axiom,
! [W: '$ki_world'] : '$ki_accessible'(W,W) ).
tff(mrel_transitive,axiom,
! [W: '$ki_world',V: '$ki_world',U: '$ki_world'] :
( ( '$ki_accessible'(W,V)
& '$ki_accessible'(V,U) )
=> '$ki_accessible'(W,U) ) ).
tff(d_decl,type,
d: $i ).
tff(n_decl,type,
n: $i ).
tff(o_decl,type,
o: $i ).
tff(h_decl,type,
h: ( '$ki_world' * $i ) > $o ).
tff(closed_decl,type,
closed: ( '$ki_world' * $i ) > $o ).
tff(combo_decl,type,
combo: ( '$ki_world' * $i * $i ) > $o ).
tff(open_decl,type,
open: ( '$ki_world' * $i ) > $o ).
tff('$ki_exists_in_world_$i_decl',type,
'$ki_exists_in_world_$i': ( '$ki_world' * $i ) > $o ).
tff('$ki_exists_in_world_$i_const',axiom,
! [W: '$ki_world',X: $i] : '$ki_exists_in_world_$i'(W,X) ).
tff('$ki_exists_in_world_$i_nonempty',axiom,
! [W: '$ki_world'] :
? [X: $i] : '$ki_exists_in_world_$i'(W,X) ).
tff(ax1,axiom,
! [W: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',W)
=> ! [S: $i] :
( '$ki_exists_in_world_$i'(W,S)
=> ! [V: $i] :
( '$ki_exists_in_world_$i'(W,V)
=> ? [O: $i] :
( '$ki_exists_in_world_$i'(W,O)
& ! [W0: '$ki_world'] :
( '$ki_accessible'(W,W0)
=> ( ( closed(W0,S)
& combo(W0,S,V)
& h(W0,O) )
=> ! [W1: '$ki_world'] :
( '$ki_accessible'(W0,W1)
=> open(W1,S) ) ) )
& ! [W0: '$ki_world'] :
( '$ki_accessible'(W,W0)
=> ( ( closed(W0,S)
& ~ combo(W0,S,V)
& h(W0,o) )
=> ! [W1: '$ki_world'] :
( '$ki_accessible'(W0,W1)
=> closed(W1,S) ) ) ) ) ) ) ) ).
tff(ax2,axiom,
! [W: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',W)
=> closed(W,d) ) ).
tff(ax3,axiom,
! [W: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',W)
=> ( combo(W,d,n)
| ~ combo(W,d,n) ) ) ).
tff(ax4,axiom,
! [W: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',W)
=> ! [S: $i] :
( '$ki_exists_in_world_$i'(W,S)
=> ~ ( open(W,S)
& closed(W,S) ) ) ) ).
tff(ax5,axiom,
? [V: $i] :
( '$ki_exists_in_world_$i'('$ki_local_world',V)
& ! [W: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',W)
=> combo(W,d,V) ) ) ).
tff(verify,conjecture,
! [W: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',W)
=> ? [V: $i] :
( '$ki_exists_in_world_$i'(W,V)
& ? [O: $i] :
( '$ki_exists_in_world_$i'(W,O)
& ( ! [W0: '$ki_world'] :
( '$ki_accessible'(W,W0)
=> ( combo(W0,d,V)
& h(W0,O) ) )
=> ! [W0: '$ki_world'] :
( '$ki_accessible'(W,W0)
=> open(W0,d) ) ) ) ) ) ).
%------------------------------------------------------------------------------